BUG - Notebook naming with Project Site Templates
This is happening with Project Online but I recall it happening with Project Server as well. Whenever you create a Project Site template and associate it with an EPT, the notebook naming convention does NOT change. It maintains the original name. THis is confusing and it means that we can't name the template anything particularly unique because every Project Manager freaks out that the notebook is wrong. And, the question is as to whether or not the notes are all sitting on the one single file or if they are sitting in the actual project. Also, this happens REGARDLESS if "enable content" is checked when creating the Project Site template. The example attached is about how the template name stays attached to the notebook.
Erock P3 commented
Have to check if you started your template from an existing project site or directly via SharePoint (not generated via project)? I have not seen this problem as you describe. I use the SharePoint method - so that my template is never associated to any project before it is used in EPT. Please try that method and let me know.